Is Earth as smooth as a billiard ball? No, here’s why

You may have heard it has been said that if our planet were shrunk down to the size of a billiard ball, it would be smoother than it. In other words, the Earth is smoother than a billiard ball. Is that true?

Back in 2008, on the “Bad Astronomy” blog on discovermagazine.com, in the article titled “Ten things you don’t know about the Earth“, Phil Plait wrote about that, and he said “…according to the World Pool-Billiard Association, a pool ball is 2.25 inches in diameter and has a tolerance of +/- 0.005 inches.” and after making some calculations, he concluded that “… the urban legend is correct. If you shrank the Earth down to the size of a billiard ball, it would be smoother.”

Even the famous American astrophysicist, author and science communicator Neil deGrasse Tyson once tweeted about that, saying “If shrunk to a few inches across, Earth would feel as smooth as a billiard-hall cue ball.”.

SMOOTH EARTH: If shrunk to a few inches across, Earth would feel as smooth as a billiard-hall cue ball.

In fact, the Earth is much smoother than one might think. Yes, there are big mountains like the Himalayas and big trench under the oceans like the Mariana Trench. The highest point on Earth is the top of Mount Everest, at 8.85 km. The deepest point on Earth is the Mariana Trench, at about 11 km deep. But even those are very small compared to the Earth’s a diameter which is about 12,735 kilometers (on average).

According to the World Pool-Billiard Association, “All balls must be composed of cast phenolic resin plastic and measure 2 1/4 (±.005) inches [5.715 cm (± .127 mm)] in diameter”.

So, if we could shrink the Earth to the size of a billiard ball, the height of Mount Everest would be only 0.04 millimeters. The depth of Mariana Trench would be only 0.045 millimeters. These measurements are inside 0.127 mm or 0.005 inches, no pits or bumps more than that, so the Earth is smoother than a billiard ball, right?

Wrong.

First of all, the specifications of the World Pool-Billiard Association does not say “there mustn’t be pits or bumps more than .005 inches”. This is only about diameter, the rule says that the diameter must be within 2 1/4 (± .005) inches. Smoothness is a very different thing.

Let’s we assume that we produced a billiard ball and covered its surface with medium sandpaper (grit particle size of 0.005 in, for more about grit sizes of a sandpaper see the Grit size table on the Wikipedia entry of sandpaper). By the definition of smoothness used by Phil Plait of Discover Magazine and Neil deGrasse Tyson, that billiard ball would also be “smooth” – which is obviously ridiculous.

The billiard-ball sized Earth’s smoothness would be equivalent to that of 320 grit sandpaper. Still not quite smooth, right?

So, it’s obvious that 0.005 inches (0.127 mm) official tolerance is for shape, for roundness, not for smoothness.

The billiard-ball sized Earth’s smoothness would be equivalent to that of 320 grit sandpaper. Image: “320 grit silicon carbide sandpaper, with close-up view” on wikipedia.

Human fingers are very sensitive

According to a 2013 study titled “Feeling Small: Exploring the Tactile Perception Limits” published on Nature, a human finger can feel wrinkles as small as 10nm (nanometers), or 0.00001 millimeters, demonstrating that human tactile discrimination extends to the nanoscale. So, if the Earth were shrunk down to the size of a billiard ball, you would definitely feel the Mount Everest, which would be 0.04 millimeters high.

As round as a billiard ball

Speaking of roundness, is Earth as round as a billiard ball?

Earth’s equatorial diameter is 7,926 miles (12,756 km), but from pole to pole, the diameter is 7,898 miles (12,714 km) – a difference of only 28 miles (42 km).

If we take the bigger diameter and shrink it down, the difference would be 0.0049 inches (0.0125 mm). If we take the smaller diameter, the difference would be very slightly bigger, but almost the same. So yes, the Earth is as round as a billiard ball. But it’s almost at the limit.

Summary

Is the Earth as smooth as a billiard ball? Answer: No.

Is the Earth as round as a billiard ball? Answer: Yes.

You can also watch Vsauce’s great video titled How Much of the Earth Can You See at Once?, which also covers this very subject.

How Much of the Earth Can You See at Once? by Vsauce. In the video, at 14:40, Michael says “you may have heard it said that if the entire planet were shrunk down to the size of a billiard ball, it would be smoother than a billiard ball. … That seems believable, but as it turns out, it’s not true. The misconception stems from the interpretation of the World Pool-Billiard Association’s rules. According to them, a billiard ball must have a diameter of 2.25 in ±0.005 in. Some writers have taken this to mean that pits and bumps of ±0.005 in are allowed. Proportionally, on Earth, that would mean a mountain that was 28 km high. So, since Earth has none of those, it must be smoother than a billiard ball. Except, if bumps that high are actually allowed on a pool ball. A ball covered with 120 grit sandpaper would be within regulation. Clearly, the ±0.005 inches rule is more about roundness, deviation from a sphere, and not the texture.”

As you can see the video above, as microscopic photography shown, imperfections on a billiard ball are only 1/100,000 inches, or about 0.5 μm deep and high. Scaled down to the size of a billiard ball, Earth’s Mariana trench would be 49 μm deep.

Let’s think it in another way: If a billiard ball was scaled up to Earth size, the difference between the highest peak and lowest point would be 14 meters (46 feet) at maximum. The billiard ball is way smoother than the Earth.

Sources

Ten things you don’t know about the Earth, “Bad Astronomy” blog by Phil Plait on discovermagazine.com

4 thoughts on “Is Earth as smooth as a billiard ball? No, here’s why”

Since you’re talking about Earth and billiards, I’d like to point out that Earth is about 3400 times flatter than a regulation pool table. (Calculating the bulge of a 4′ x 8′ section of a sphere with radius of 6371 meters gives 146 nanometers compared to requirement of +/-0.5mm per WPA & BCA)

I am curious, I’m not 100% sure how all of this works so i could be wrong but the measure of smoothness is also related to the proximity of these height differences right? So your sandpaper example implies that the highest and lowest points of the planet repeat over and over again outwards from a single point(up, down, up, down, up, down) . There is only one point that is the highest and another point that is the lowest with some distance in between, it’s not like there is a mountain and trench tangent every x amount of distance consecutively. The rest of the height differences in the geography are much smaller over a larger area. Am I not thinking of this correctly? This is a really cool idea whether its true or not =)

Thanks for the comment. For some places in the world, you’re right. But a lot of other places, there are big differences in elevation. The Himalayas is just an example, also the Alps. For instance, Nanga Parbat’s Rupal Face rises approximately a whopping 4,600 meters, or 15,000 feet, above its base. You would definitely feel it if the Earth were shrunk down to the size of a billiard ball.